We began haveing black spots on the sunflower leaves, starting at the tip of the leaf and gradually moving inward.  The leaves would turn black on the top but still be somewhat alive on the bottom.

I cut a leaf off and took it inside.  Observations showed that the leave was wiggling.  There was a larve crawling in the leaf, eatting its way towards the stalk.

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To remedy this, I quickly cut off the leaves that were affected and then sprayed soap water on the leaves.  I believe that this has slowed their spread, though  I still need to find out what the larve is.